I'll jump in here (apologies to Garth if this isn't what you're talking about). I've trained with Ikeda sensei as often as I can over the past 10 years now, he's now beginning to make a little more sense (to me) and earlier this year he explained some of what he's doing... I can do this a little with my own students on a very basic level so I'll try and explain one of the 'both facing the same direction' examples.

Uke makes a fist and sticks his arm out to his side (kind of like someone thumbing a lift), nage touches or cups uke's fist and 'makes a line' to uke. I asked Ikeda sensei a number of times to explain what make a line meant, he kept telling me it was just a line. Rightly or wrongly I think about it being ever so slightly me taking out any slack, not leaning on my partner but getting closer to them, hard to explain. So, once I've made my line, I then move my center which displaces uke's center and I can usually see a small movement in my partner as if I've just 'bumped' him a little. Once this has happened, I can move him around, make him fall over etc. How do I move my center? Well, again, finally this year I got some help on that one from Ikeda sensei. I'll try and explain...

You stand kind of relaxed, neutral. You move your stomach in a circular direction, up and forward and slightly down (forward) then reverse (center) then up and back (back) then reverse (center) then up and left (left) then reverse (center) then up and right (right) then reverse. I can't really explain this that well, but after doing this a good few times you feel slightly strange inside... Ikeda sensei said you need to do this everyday, practice, you don't need a partner. I find it great to do when driving, and I had hold of the steering wheel, I *think* I can feel my center moving around and I feel heavier on one side etc. It's almost like the movement body poppers used to make way back when, that line, squiggle, wave form shape.

He's also done the same exercise with him sat in a chair to me...

This is all probably badly explained but it's all I've got to work on at the moment, again, I'll say I can get this to work on my students and visitors to my club but I'm really not sure exactly how it's working. I've tried to explain what's in my head when I'm doing it based on talking to Ikeda sensei.